Answer: Choice D
11pi/4
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Step-by-step explanation:
The angles shown add to: 120+45+30 = 195 degrees.
The remaining bit needed to get to a full 360 degree circle is 360-195 = 165 degrees, which is the measure of central angle AFD.
This means the arc AED is 165/360 of the full circle perimeter or circumference.
The fraction 165/360 reduces to 11/24 after dividing both parts by the GCF 15
So we can say that the length of arc AED is exactly 11/24 of the full circumference.
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The length FB is 3 units (radius), so EB is 6 units (diameter)
This leads to,
C = circumference
C = pi*diameter
C = pi*6
C = 6pi
That's the full circumference, but we only want 11/24 of it to get arc AED.
arc AED = (11/24)*(full circumference)
arc AED = (11/24)*(6pi)
arc AED = 11pi/4 which is choice D
I'm assuming choice D says 11pi/4